Circular cylinder translational flow

Low Reynolds numbers. In [216, 382] the problem on a circular cylinder of radius a in translational flow of viscous incompressible fluid with velocity Ul at low Reynolds numbers was solved by the method of matched asymptotic expansions. The study was carried out on the basis of the Navier-Stokes equations (1.1.4) in the polar coordinates 1Z, 6. Thus, the following expression for the stream function was obtained for IZ/a 1 ... 

Circular cylinder. The mass exchange between a circular cylinder of radius a and a uniform translational flow whose direction is perpendicular to the generatrix of the cylinder was considered in [186,218] for low Peclet and Reynolds numbers Pe = Sc Re and Re = aU-Jv. For the mean Sherwood number (per unit length of the cylinder) determined with respect to the radius, the following two-term expansions were obtained ... 

At high Peclet numbers, for an nth-order surface reaction withn=l/2, 1,2, Eq. (5.1.5) was tested in the entire range of the parameter ks by comparing its root with the results of numerical solution of appropriate integral equations for the surface concentration (derived in the diffusion boundary layer approximation) in the case of a translational Stokes flow past a sphere, a circular cylinder, a drop, or a bubble [166, 171, 364], The comparison results for a second-order surface reaction (n = 2) are shown in Figure 5.1 (for n = 1/2 and n = 1, the accuracy of Eq. (5.1.5) is higher than for n = 2). Curve 1 (solid line) corresponds to a second-order reaction (n = 2). One can see that, the maximum inaccuracy is observed for 0.5 < fcs/Shoo < 5.0 and does not exceed 6% for a solid sphere (curve 2), 8% for a circular cylinder (curve 3), and 12% for a spherical bubble (curve 4). 

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